Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.Author Summary: In recent years, sleep has drawn increasing attention due to its multifunctional role, e.g. the involvement in the consolidation of memory. While neural mass models have been successfully employed to describe the dynamics of the awake brain, the drastic changes that arise during sleep have been challenging. As intracellular recordings point to a bistability in the membrane voltage of individual neurons, previous studies assumed a bistability to be responsible for the generation of SOs as well as KCs on the macroscopic scale. Here we present a minimal neural mass model of the cortex that we extend by a slow firing rate adaptation, which is assumed to underlie the termination of the cortical up state. A bifurcation analysis reveals the existence of a Hopf bifurcation together with an canard phenomenon. We show that these additional bifurcations are able to generate KCs as well as SOs, and reproduce the electroencephalogram (EEG) of sleeps stages N2 and N3 to a high degree. Based on these findings, we propose a new route for the sleep/wake transition, that is also consistent with the effect of neuromodulators on the brain.